I don't go to UT but my boyfriend is in a fraternity there. The great thing about UT is that Greek life is strong but does not dominate campus life. College board says only 14% of women join sororities at UT. I'm not sure how accurate that is but if it is close to the actual amount, then you will meet LOTS of girls who aren't in sororities. Another great thing is that UT has some awesome women's organizations that aren't traditional NPC sororities, but they have similar functions. For example, Texas Spirits has been around campus for over 60 years. They do a lot of school spirit activities such as painting the windows of local businesses with longhorns and stuff. They get dressed up for the games in "Spirit attire" and I've heard it's really fun. There's also Texas Lonestars, Wrangler Darlings, Texas Honeys, Lassos, etc. These organizations have mixers with the fraternities on campus just like sororities do.
Here is the website for Spirits
http://studentorgs.utexas.edu/spirits/
Wrangler Darlins
http://www.wranglerdarlins.org/
Lassos
http://studentorgs.utexas.edu/txlassos/
Lonestars
http://www.texas-lonestars.com/spirit.html
Don't let the competitive nature of greek life at UT scare you! UT is a great school with a good campus life, greek or otherwise.